The Andersonian Museum developed out of the collection of scientific apparatus and natural history specimens collected by John Anderson and bequeathed by him, in 1796, to Anderson's Institution. This formed the nucleus of the Museum's collections to which were added other specimens illustrative of local natural history. The aim of the Museum was to provide a general collection in which every department of natural history was represented and each specimen named so that the student, by aid of the catalogue, could become his own teacher. It was considered that natural history was the area best calculated to promote a taste for science.
The mid-nineteenth century was a period of remarkable expansion, and the Museum attracted many donations from trustees, students, teachers and others. There was a fine collection of stuffed birds, and the collection of coins, antiquities, and other curiosities was extensive and valuable. The designer of the Museum's building, James Smith, of Jordanhill, President of Anderson's University, also donated coins and medals and Thomas Eddington II presented mineral specimens, animals and birds. The gallery devoted to birds included 2,000 specimens bought from Joseph Sabine, and in 1860, Professor Robert Hunter gave the Museum a thousand anatomical specimens on the occasion of his retirement. Specimens also came from the British Association for the Advancement of Science (collection of fossils and minerals), the Glasgow Dilettanti Society (its collection of models on permanent loan), Dr James Couper (1150 mineral specimens, 500 foreign shells, 140 British shells), the Lord Commissioners of the Treasury (a group of Roman, Anglo-Saxon, and ancient Scottish coins discovered in 1851), and James Scouller (Natural History specimens).
In 1856, one of the Museum's benefactors, William Euing, proposed the building of an extension. Money was raised with the help of Euing and his friends, and the final refitting of the cupola and reordering of the Museum was in progress by November 1862.
By the 1870s, however, the Museum began to pass into decline. Visitor numbers were falling and the negotiations for the formation of the Glasgow and West of Scotland Technical College and the move towards more technical subjects rendered the collections of little value for teaching purposes. In addition, there was pressure on accommodation and, in 1882, the ground floor of the Museum was converted into a reading room and the collections relegated to the galleries. In 1887, a decision was made to transfer to other museums all the collections not required for teaching purposes. Most of the ethnographic collections were given to the Hunterian Museum at Glasgow University whilst the coin collections and much else went to the Kelvingrove Museum. The Museum ceased to exist about 1900. A few items, such as John Anderson's musket and dirk remain at the University of Strathclyde.